Time Series Basics and Operators
T. H. Merrett · 2008
Subtracting the average reduces the dimension of the space by 1, because there is now a linear dependence among the coefficients of a vector v : v1 + v2 + ..vn = 0. In two dimensions, a vector (c, s) becomes c−s 2 (1,−1): everything maps into the line (1,−1). In three dimensions, everything maps into the subspace orthogonal to (1,1,1). If its basis vectors are B1 = 1 √ 2 (1,−1, 0) and B2 = 1 √ 6 (1, 1,−2), then we have the mappings